Illuminating devices, in particular those in which semiconductor light sources, such as LEDs, are used for light generation, are often formed in a modular manner, that is to say different modules having different functions are provided. Here, what are known as the lighting modules, that is to say the modules that basically carry the actual light sources, are of central importance. These modules are to be easily mountable, but at the same time are to be held reliably and are to have a good transfer of heat to the lighting module support arranged therebelow in order to be able to reliably dissipate the heat produced during operation of the light sources. For this purpose, the lighting modules are usually screwed or adhesively bonded to the lighting module carrier, such that the mechanical contact is ensured. A disadvantage however of an adhesive bond is that the module can only be removed with difficulty from the support or may no longer be removable at all from the support. By contrast, in the case of a screw or rivet connection, the lighting module can indeed be separated again easily from the support, however it is fixed by the screws at the screw holes such that, with heating, the lighting module may bulge due to the different thermal expansion of modules and support, and therefore the thermal connection to the support is impaired or interrupted and the module may overheat. The module may also sustain mechanical damage due to the bulging. In order to improve the thermal contact between lighting module and module support, what is known as a thermal interface material (TIM) is often introduced between the lighting module and lighting module support and improves the thermal contact in particular by compensating for unevennesses. This is complex however and also may not ensure the thermal contact in the event of excessive bulging of the module.